James Gillooly of the University of Florida in Gainesville, US, and
colleagues started with an equation showing the relationship between body
size, body temperature and growth rate of an animal.
They then applied this equation, which has been shown to be valid across a
variety of living species, to dinosaurs.

"*Syntarsus [sic!] rhodesiensis*, *Psittacosaurus mongoliensis*,
*Apatosaurus excelsus*, *Tyrannosaurus rex*, *Daspletosaurus torosus*,
*Gorgosaurus libratus*, *Albertosaurus sarcophagus*, and *Massospondylus
carinatus*" "ranged in adult size from 15" to "25,952 kg". Hm. Apart from
the useless precision, where is the 26-tonner in this sample? It can't be
*Apatosaurus* which is said to be half as heavy later in the paper, to be
precise, 12,979 kg. Along the same lines I wonder if 15 kg is too much for
*Psittacosaurus mongoliensis*. Indeed -- later in the same paper this
species is said to have 12 kg (...which still strikes me as much). But
perhaps there's just another typo in there. *Albertosaurus sarcophagus* was
both 614 and 218 kg heavy, according to two adjacent sentences.
Peer-reviewers? Editors?

*Shuvuuia deserti* "was excluded from our analysis because it is a feathered
species and is therefore fundamentally different than the eight more
reptile-like species mentioned above." Well. As an alvarezsaur it probably
is more closely related to the (other?) birds than all of the studied
species are. But still, Gillooly et al. are preassuming the conclusion
here.
This is not science. What did I just say about the peer-reviewers and
editors? Oh, I haven't even mentioned *Dilong* yet -- a tyrannosaur as
feathered as *Shuvuuia*.

"Specifically, we analyze these data using a recently published model that
predicts the combined effects of body size and temperature, T(b) (°C), on
maximum growth rate (12,13):
[Equation 1]
Equation 1 builds on a previously published model that predicts growth rates
for a broad assortment of ectotherms and endotherms (14). It has now been
used successfully to predict rates of embryonic growth in diverse taxa
(13),
rates of post-embryonic growth in zooplankton (13), rates of
individual-level biomass production (15), and rates of population-level
growth in diverse taxonomic groups (16)."

I went through ref. 14
(http://www.nature.com/nature/journal/v413/n6856/abs/413628a0.html;
probably
free access) -- I can't quite see through all the math, but it doesn't
mention temperature at all. Gillooly et al. don't say that any of the other
refs test if the formula predicts post-embryonic individual growth of
anything. Unfortunately I don't have time to go through the other refs, so
I
can't check if this equation really holds for all the diversity of
endothermic animals.

According to the scientists' equation, the enormous sauropod Apatosaurus -
which at 13,000kg was among one of the biggest dinosaurs - had a body
temperature of just over 40C.

Now, where does that leave the many sauropods that were undoubtedly bigger
and heavier than *Apatosaurus*? Gillooly et al. answer this question: "If
we
extrapolate the model depicted in Figure 1 up to what is perhaps the
largest
dinosaur species (55,000 kg for an adult *Sauroposeidon proteles* (23)),
the
estimated body temperature at the mass of maximum growth is approximately
48
°C, which is just beyond the upper limit tolerated for most animals ( ~ 45
°C).
These findings suggest that maximum dinosaur size may have ultimately been
limited by body temperature." Wwwellll. Whales?

Someone who is less tired and more at home in math and physics should read
through "Estimating g(0)" in the Materials and Methods section. To me it
seems to say that dinosaurs were preassumed to be intermediate between
mammals and "reptiles" in an important way.